Design an Adaptive Sliding Mode Controller for a Class of Underactuated Systems

Subject Areas : vibration and control

Hossein  Moeinkhah ¹ (Department of Mechanical Engineering, Shahid Nikbakht Faculty, University of Sistan and Baluchestan, Zahedan, Iran.)
Mohammad  Ahmadi Balootaki ² (Department of Mechanical Engineering, Shahid Nikbakht Faculty, University of Sistan and Baluchestan, Zahedan, Iran. Faculty of Shahid Bahonar, Sistan and Baluchestan Branch, Technical and Vocational University (TVU), Zahedan, Iran.)

Received: 2020-04-23 Accepted : 2020-09-02 Published : 2021-12-01

Keywords: Stability Analysis, Adaptive Sliding Mode Control, Robust controller, Underactuated Systems, Multi-Objective Non-Dominated Sorting,

Abstract :

The majority of underactuated systems are nonholonomic, due to non-integrable differential constraints. Therefore, controlling an underactuated system is considered as a challenging problem. In this study, an adaptive controller based on super-twisting sliding mode controller is proposed for a class of robust underactuated systems subjected to uncertainties and external disturbances. The adaptive compensator was designed so that there would be no need to the upper bound of the external disturbance. The controller parameters of adaptive sliding mode control are tuned based on a multi-objective non-dominated sorting of genetic optimization algorithm. The results of simulation and the demonstration of the effectiveness and applicability of the proposed scheme are presented.

References:

• Khan, Q., Akmeliawati, R., Bhatti, A. I., and Khan, M. A., Robust Stabilization of Underactuated Nonlinear Systems: A Fast Terminal Sliding Mode Approach, ISA Transactions, 66, No. 1, 2017, pp. 241-248.


• Ye, L., Zong, Q., Tracking Control of an Underactuated Ship by Modified Dynamic Inversion, ISA Transactions, 83, No. 5, 2018, pp. 100-106.


• Tian, Z., Wu, H., and Feng, C., Hierarchical Adaptive Backstepping Sliding Mode Control for Underactuated Space Robot, in 2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR 2010), Vol. 1, IEEE, 2010, pp. 500-503.


• Muniandy, M., Muthusamy, K., An Innovative Design to Improve Systematic Odometry Error in Non-Holonomic Wheeled Mobile Robots, Procedia Engineering, 41, No. 1, 2012, pp. 436-442.


• Oryschuk, P., Salerno, A., Al-Husseini, A. M., and Angeles, J., Experimental Validation of an Underactuated Two-Wheeled Mobile Robot, IEEE/ASME Transactions on Mechatronics, 14, No. 2, 2009, pp. 252-257.


• Woods, S. A., Bauer, R. J., and Seto, M. L., Automated Ballast Tank Control System for Autonomous Underwater Vehicles, IEEE Journal of Oceanic Engineering, 37, No. 4, 2012, pp. 727-739.


• Aguiar, A. P., Hespanha, J. P., Trajectory-Tracking and Path-Following of Underactuated Autonomous Vehicles with Parametric Modeling Uncertainty, IEEE Transactions On Automatic Control, 52, No. 8, 2007, pp. 1362-1379.


• Ge, S. S., Lee, T. H., and Zhu, G., Genetic Algorithm Tuning of Lyapunov-Based Controllers: An Application to A Single-Link Flexible Robot System, IEEE Transactions on Industrial Electronics, 43, No. 5, 1996, pp. 567-574.


• Hussein, I. I., Bloch, A. M., Optimal Control of Underactuated Nonholonomic Mechanical Systems, IEEE Transactions on Automatic Control, 53, No. 3, 2008, pp. 668-682.


• Spong, M. W., The Swing Up Control Problem for The Acrobot, IEEE Control Systems Magazine, 15, No. 1, 1995, pp. 49-55.


• Spong, M. W., Modeling and Control of Elastic Joint Robots, ASME, Vol. 109, No. 4, 1987, pp. 310-318.


• Chen, Y. F., Huang, A. C., Controller Design for A Class of Underactuated Mechanical Systems, IET control theory & applications, 6, No. 1, 2012, pp. 103-110.


• Man, W. S., Lin, J. S., Nonlinear Control Design for A Class of Underactuated Systems, in 2010 IEEE International Conference on Control Applications, IEEE, 2010, pp. 1439-1444.


• Olfati-Saber, R., Nonlinear Control of Underactuated Mechanical Systems With Application to Robotics and Aerospace Vehicles, Ph.D, Massachusetts Institute of Technology, 2001.


• Ravichandran, M. T., Mahindrakar, A. D., Robust Stabilization of a Class of Underactuated Mechanical Systems Using Time Scaling and Lyapunov Redesign, IEEE Transactions on Industrial Electronics, 58, No. 9, 2010, pp. 4299-4313.


• Reyhanoglu, M., Van Der Schaft, A., McClamroch, N. H., and Kolmanovsky, I., Nonlinear Control of a Class of Underactuated Systems, in Proceedings of 35th IEEE Conference on Decision and Control, Vol. 2, 1996, IEEE, pp. 1682-1687.


• Spong, M. W., Underactuated Mechanical Systems, In Control Problems in Robotics and Automation: Springer, 1998, pp. 135-150.


• Zhou, K., Doyle, J. C., and Glover, K., Robust and Optimal Control, Prentice hall New Jersey, 1996.


• Sciavicco, L., Siciliano, B., Modelling and Control of Robot Manipulators, Springer Science & Business Media, 2012.


• Slotine, J. J., Coetsee, J., Adaptive Sliding Controller Synthesis for Non-Linear Systems, International Journal of Control, 43, No. 6, 1986, pp. 1631-1651.


• Yao, B., Tomizuka, M., Robust Adaptive Motion and Force Control of Robot Manipulators in Unknown Stiffness Environments, In Proceedings of 32nd IEEE Conference on Decision and Control, IEEE, 1993, pp. 142-147.


• Yao, B., Tomizuka, M., Adaptive Robust Control of SISO Nonlinear Systems in A Semi-Strict Feedback Form, Automatica, 33, No. 5, 1997, pp. 893-900.


• Yao, B., Bu, F., Reedy, J., and Chiu, G. C., Adaptive Robust Motion Control of Single-Rod Hydraulic Actuators: Theory and Experiments, IEEE/ASME transactions on mechatronics, 5, No. 1, 2000, pp. 79-91.


• Yao, B., Bu, F., and Chiu, G. T. C., Non-Linear Adaptive Robust Control of Electro-Hydraulic Systems Driven by Double-Rod Actuators, International Journal of Control, 74, No. 8, 2001, pp. 761-775.


• Mirzaei, M., Nia, F. S., and Mohammadi, H., Applying Adaptive Fuzzy Sliding Mode Control to an Underactuated System, In The 2nd International Conference on Control, IEEE, 2011 Instrumentation and Automation, pp. 654-659.


• Din, S. U., Khan, Q., Rehman, F. U., and Akmeliawanti, R., A Comparative Experimental Study of Robust Sliding Mode Control Strategies for Underactuated Systems, IEEE Access, Vol. 5, 2017, pp. 10068-10080.


• Yan, Z., Wang, M., and Xu, J., Robust Adaptive Sliding Mode Control of Underactuated Autonomous Underwater Vehicles with Uncertain Dynamics, Ocean Engineering, Vol. 173, 2019, pp. 802-809.


• Gurumurthy, G., Das, D. K., Terminal Sliding Mode Disturbance Observer Based Adaptive Super Twisting Sliding Mode Controller Design for a Class of Nonlinear Systems, European Journal of Control, 2020.


• Jmel, I., Dimassi, H., Hadj-Said, S., and M’Sahli, F., An Adaptive Sliding Mode Observer for Inverted Pendulum Under Mass Variation and Disturbances with Experimental Validation, ISA Transactions, 2020.


• Deng, M., Inoue, A., and Shimizu, T., Combined Attitude Control of an Underactuated Helicopter Experimental System, In Proc. of UKACC International Conference on Control, 2008.


• Lee, D., Kim, H. J., and Sastry, S., Feedback linearization vs. Adaptive Sliding Mode Control for A Quadrotor Helicopter, International Journal of Control, Automation and Systems, Vol. 7, No. 3, 2009, pp. 419-428.


• Keymasi Khalaji, A., and Moosavian, S. A. A., Adaptive Sliding Mode Control of a Wheeled Mobile Robot Towing a Trailer, Proceedings of The Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, Vol. 229, No. 2, 2015, pp. 169-183.


• Su, G. J., Gong, Q. L., and Li, H. Y., Adaptive Sliding-Mode Control Based On Decoupled Method for A Class of Underactuated System, In 2017 36th Chinese Control Conference (CCC), IEEE, 2017, pp. 639-643.


• Liu, W., Chen, S., and Huang, H., Actor-Critic Learning Hierarchical Sliding Mode Control for a Class of Underactuated Systems, In 2019 Chinese Automation Congress (CAC), IEEE, 2019, pp. 1-6.


• Ovalle, L., Ríos, H., and Llama, M., Continuous Sliding-Mode Control for a Class of Underactuated Systems, In 2019 IEEE 58th Conference on Decision and Control (CDC), IEEE, 2019, pp. 6001-6006.


• Rangel, M. A. G., Manzanilla, A., Suarez, A. E. Z., Muñoz, F., Salazar, S., and Lozano, R., Adaptive Non-singular Terminal Sliding Mode Control for an Unmanned Underwater Vehicle: Real-time Experiments, International Journal of Control, Automation and Systems, Vol. 18, No. 3, 2020, pp. 615-628.